Problem: Simplify the following expression: $\dfrac{84p^2}{42p^5}$ You can assume $p \neq 0$.
Explanation: $ \dfrac{84p^2}{42p^5} = \dfrac{84}{42} \cdot \dfrac{p^2}{p^5} $ To simplify $\frac{84}{42}$ , find the greatest common factor (GCD) of $84$ and $42$ $84 = 2 \cdot 2 \cdot 3 \cdot 7$ $42 = 2 \cdot 3 \cdot 7$ $ \mbox{GCD}(84, 42) = 2 \cdot 3 \cdot 7 = 42 $ $ \dfrac{84}{42} \cdot \dfrac{p^2}{p^5} = \dfrac{42 \cdot 2}{42 \cdot 1} \cdot \dfrac{p^2}{p^5} $ $\phantom{ \dfrac{84}{42} \cdot \dfrac{2}{5}} = 2 \cdot \dfrac{p^2}{p^5} $ $ \dfrac{p^2}{p^5} = \dfrac{p \cdot p}{p \cdot p \cdot p \cdot p \cdot p} = \dfrac{1}{p^3} $ $ 2 \cdot \dfrac{1}{p^3} = \dfrac{2}{p^3} $